Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays

The goal of this paper is to introduce a new method in computer-aided geometry of solid modeling. We put forth a novel algebraic technique to evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with regularized operators of union, intersection, and difference, i.e., any CSG tree. The result is obtained in three steps: first, by computing an independent set of generators for the d-space partition induced by the input; then, by reducing the solid expression to an equivalent logical formula between Boolean terms made by zeros and ones; and, finally, by evaluating this expression using bitwise operators. This method is implemented in Julia using sparse arrays. The computational evaluation of every possible solid expression, usually denoted as CSG (Constructive Solid Geometry), is reduced to an equivalent logical expression of a finite set algebra over the cells of a space partition, and solved by native bitwise operators.Comment: revised version submitted to Computer-Aided Geometric Desig

Proceedings of the Workshop Semantic Content Acquisition and Representation (SCAR) 2007

This is the proceedings of the Workshop on Semantic Content Acquisition and Representation, held in conjunction with NODALIDA 2007, on May 24 2007 in Tartu, Estonia.</p

Using Sparse Semantic Embeddings Learned from Multimodal Text and Image Data to Model Human Conceptual Knowledge

Distributional models provide a convenient way to model semantics using dense embedding spaces derived from unsupervised learning algorithms. However, the dimensions of dense embedding spaces are not designed to resemble human semantic knowledge. Moreover, embeddings are often built from a single source of information (typically text data), even though neurocognitive research suggests that semantics is deeply linked to both language and perception. In this paper, we combine multimodal information from both text and image-based representations derived from state-of-the-art distributional models to produce sparse, interpretable vectors using Joint Non-Negative Sparse Embedding. Through in-depth analyses comparing these sparse models to human-derived behavioural and neuroimaging data, we demonstrate their ability to predict interpretable linguistic descriptions of human ground-truth semantic knowledge.Comment: Proceedings of the 22nd Conference on Computational Natural Language Learning (CoNLL 2018), pages 260-270. Brussels, Belgium, October 31 - November 1, 2018. Association for Computational Linguistic

Exploiting Low-dimensional Structures to Enhance DNN Based Acoustic Modeling in Speech Recognition

We propose to model the acoustic space of deep neural network (DNN) class-conditional posterior probabilities as a union of low-dimensional subspaces. To that end, the training posteriors are used for dictionary learning and sparse coding. Sparse representation of the test posteriors using this dictionary enables projection to the space of training data. Relying on the fact that the intrinsic dimensions of the posterior subspaces are indeed very small and the matrix of all posteriors belonging to a class has a very low rank, we demonstrate how low-dimensional structures enable further enhancement of the posteriors and rectify the spurious errors due to mismatch conditions. The enhanced acoustic modeling method leads to improvements in continuous speech recognition task using hybrid DNN-HMM (hidden Markov model) framework in both clean and noisy conditions, where upto 15.4% relative reduction in word error rate (WER) is achieved